
As a result of the classical invariant theory [1]}, the first non-zero fundamental invariant of degree 6 can be constructed via Cayley's \(\Omega \)  process as [2]}
\(I_6\equiv \frac{1}{1152}\operatorname{tr}\Omega _x^2\Omega _y^2\Omega _z^2\prod _{i=1}^3f^2(\mathbf {x}^{(i)},\mathbf {y}^{(i)},\mathbf {z}^{(i)}),\) 
